Abstract

Extensive experimental work has been carried out to characterize the stable Na-vacancy ordering patterns at various compositions of layered . However, contradictions and debates prevail in the literature, particularly at high Na concentrations . Understanding of the exotic electronic properties in this system requires a thorough understanding of the Na-vacancy structural orderings. Using density functional theory in the generalized gradient approximation (GGA), combined with a cluster expansion structure prediction algorithm we have found an intricate set of Na-vacancy ordered ground states in . We demonstrate a newly predicted ordering pattern between . By comparing the first principles electronic structure methods within the GGA and (Hubbard correction) approximations, we demonstrate that at certain Na concentration the stable ordering is affected by charge localization on the Co layer through coupling between the Na and Co lattices.